Please don't take this the wrong way, but I am curious why there is continued development of MP3 encoding (such as LAME) when AAC is now long-known to yield superior quality for a given bit-rate (all other things being equal)?

I can sort of understand an explanation as being for the heck of it, but given that a superior method exists, why not work on improving even that instead? I'm not technolgically sophisticated enough to comment with any authority at all, so I pose the question.

I have a question who really has performed ABX test to see if there was an improvement for LAME 3.97/3.98/3.99 for the same bitrate.

AFAIK each new version boosts more bitrate on difficult parts. That makes uncomparable 3.97 -V5 vs 3.98 -V 5. 3.99 -V0 is better than 3.98.4/3.97 -V0 because it has higher bitrate. It's ok as V0 targets to highest quality close to max 320 kbps.

But the question is: were there any substantial improvements while keeping the same bitrate?

.....I really like very much LAME project but I can't see clear improvements without increasing bitrate (since 3.97).

Sure there was improvement.Trumpet for instance was real bad when using VBR up to 3.97. 3.98 improved significantly on it. Same goes for the 'sandpaper noise' issue. Just to talk about problem samples I care about. IIRC eig improved too.Improvements like these don't necessarily bring average bitrate up. AFAIK average bitrate for the various -V levels did not significantly vary from version to version before 3.99. For 3.99 it's by design, but even then for -V levels around -V3/-V2 average bitrate is very close to that of 3.98.Of course individual birate of specific tracks can vary significantly reflecting changes in the psy model.